Discrete components of some complementary series representations
type: Item
instance of: scholarly article
title: Discrete components of some complementary series representations
zbMATH Open document ID: 1197.22008
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2010-07-09T00:00:00Z
review text: It is shown that the restriction of the complementary series representations of \(SO(n,1)\) to \( SO(m,1)~(m<n)\) contains complementary series representations of \(SO(m,1)\) discretely under certain conditions. As a consequence, it is proved that the cohomological representation of degree \(i\) of the group \(SO(n,1)\) contains discretely, for \(i\leq m/2\), the cohomological representation of degree \(i\) of the subgroup \(SO(m,1)\) for \(i\leq m/2\). As a global application, it is shown that if \(G/\mathbb{Q}\) is a semisimple algebraic group such that \(G(\mathbb{R})=SO(n,1)\) up to compact factors and if for all \(n\) the tempered cohomological representations are not limits of complementary series in the automorphic dual of \(SO(n,1)\), then for all \(n\), non-tempered cohomological representations are isolated in the automorphic dual of \(G\).
reviewed by: Osman Bizim
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 5734654
zbMATH Keywords: complementary series representations
zbMATH Keywords: Selberg eigenvalue conjecture
zbMATH Keywords: hyperbolic manifolds
author: Birgit Speh
author: T. N. Venkataramana
MaRDI profile type: Publication
full work available at URL: s13226-010-0020-2
OpenAlex ID: W2038361414
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DOI: 10.1007/S13226-010-0020-2
description: scientific article; zbMATH DE number 5734654